4 Robust Statistics and Non-Linear Methods

4.1 Data Import and Exploratory Data Analysis

4.1.1

import numpy as np 
import pandas as pd 
from statsmodels import robust
from scipy.stats import iqr
from scipy import stats

AAPL = pd.read_csv('AAPL.csv', index_col=0) 
IBM = pd.read_csv('IBM.csv', index_col=0) 
JPM = pd.read_csv('JPM.csv', index_col=0) 
DJI = pd.read_csv('DJI.csv', index_col=0)

AAPL.index = pd.to_datetime(AAPL.index)
IBM.index = pd.to_datetime(IBM.index)
DJI.index = pd.to_datetime(DJI.index)
JPM.index = pd.to_datetime(JPM.index)

vals = ['Open', 'High', 'Low', 'Close', 'Adj Close', 'Volume']
statistics = ['Mean', 'Median', 'Standard Deviation', 'Median Absolute Deviation', 'Interquartile Range']
stats_df_final = pd.DataFrame(index=statistics, columns=vals)

apple_data = AAPL.copy() 


for val in vals: 
    col = apple_data[val]
    stats_df_final[val]['Mean'] = col.mean() 
    stats_df_final[val]['Median'] = col.median()
    stats_df_final[val]['Standard Deviation'] = col.std() 
    stats_df_final[val]['Median Absolute Deviation'] = stats.median_abs_deviation(col) 
    stats_df_final[val]['Interquartile Range'] = iqr(col)

# stats_df_final.to_csv('AAPLstats.csv')

vals = ['Open', 'High', 'Low', 'Close', 'Adj Close', 'Volume']
statistics = ['Mean', 'Median', 'Standard Deviation', 'Median Absolute Deviation', 'Interquartile Range']
stats_df_final = pd.DataFrame(index=statistics, columns=vals)
ibm_data = IBM.copy() 

for val in vals: 
    col = ibm_data[val]
    stats_df_final[val]['Mean'] = col.mean() 
    stats_df_final[val]['Median'] = col.median()
    stats_df_final[val]['Standard Deviation'] = col.std() 
    stats_df_final[val]['Median Absolute Deviation'] = stats.median_abs_deviation(col) 
    stats_df_final[val]['Interquartile Range'] = iqr(col)

# stats_df_final.to_csv('IBMstats.csv')

vals = ['Open', 'High', 'Low', 'Close', 'Adj Close', 'Volume']
statistics = ['Mean', 'Median', 'Standard Deviation', 'Median Absolute Deviation', 'Interquartile Range']
stats_df_final = pd.DataFrame(index=statistics, columns=vals)
dji_data = DJI.copy() 

for val in vals: 
    col = dji_data[val]
    stats_df_final[val]['Mean'] = col.mean() 
    stats_df_final[val]['Median'] = col.median()
    stats_df_final[val]['Standard Deviation'] = col.std() 
    stats_df_final[val]['Median Absolute Deviation'] = stats.median_abs_deviation(col) 
    stats_df_final[val]['Interquartile Range'] = iqr(col)

# stats_df_final.to_csv('DJIstats.csv')

vals = ['Open', 'High', 'Low', 'Close', 'Adj Close', 'Volume']
statistics = ['Mean', 'Median', 'Standard Deviation', 'Median Absolute Deviation', 'Interquartile Range']
stats_df_final = pd.DataFrame(index=statistics, columns=vals)
jpm_data = JPM.copy() 

for val in vals: 
    col = jpm_data[val]
    stats_df_final[val]['Mean'] = col.mean() 
    stats_df_final[val]['Median'] = col.median()
    stats_df_final[val]['Standard Deviation'] = col.std() 
    stats_df_final[val]['Median Absolute Deviation'] = stats.median_abs_deviation(col) 
    stats_df_final[val]['Interquartile Range'] = iqr(col)

# stats_df_final.to_csv('JPMstats.csv')

apple_data['Simple Returns'] = apple_data['Adj Close'].pct_change() 
apple_data['Log Returns'] = np.log(apple_data['Adj Close']).diff()

ibm_data['Simple Returns'] = ibm_data['Adj Close'].pct_change() 
ibm_data['Log Returns'] = np.log(ibm_data['Adj Close']).diff()

jpm_data['Simple Returns'] = jpm_data['Adj Close'].pct_change() 
jpm_data['Log Returns'] = np.log(jpm_data['Adj Close']).diff()

dji_data['Simple Returns'] = dji_data['Adj Close'].pct_change() 
dji_data['Log Returns'] = np.log(dji_data['Adj Close']).diff()

import matplotlib.pyplot as plt 

apple_data['Simple Returns'].plot(color = 'blue')

plt.title('Simple Returns for Apple', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=12)
plt.ylabel('Simple Returns', fontname="arial", fontsize=12)
plt.xticks(fontname="arial", fontsize=10)
plt.yticks(fontname="arial", fontsize=10)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(6, 4)

# plt.savefig('4_1_1a.pdf')

apple_data['Log Returns'].plot(color = 'red')

plt.title('Log Returns for Apple', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=12)
plt.ylabel('Log Returns', fontname="arial", fontsize=12)
plt.xticks(fontname="arial", fontsize=10)
plt.yticks(fontname="arial", fontsize=10)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(6, 4)

# plt.savefig('4_1_1b.pdf')

ibm_data['Simple Returns'].plot(color = 'blue')

plt.title('Simple Returns for IBM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=12)
plt.ylabel('Simple Returns', fontname="arial", fontsize=12)
plt.xticks(fontname="arial", fontsize=10)
plt.yticks(fontname="arial", fontsize=10)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_1c.pdf')

ibm_data['Log Returns'].plot(color = 'red')

plt.title('Log Returns for IBM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=12)
plt.ylabel('Log Returns', fontname="arial", fontsize=12)
plt.xticks(fontname="arial", fontsize=10)
plt.yticks(fontname="arial", fontsize=10)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_1d.pdf')

jpm_data['Simple Returns'].plot(color = 'blue')

plt.title('Simple Returns for J.P. Morgan', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=12)
plt.ylabel('Simple Returns', fontname="arial", fontsize=12)
plt.xticks(fontname="arial", fontsize=10)
plt.yticks(fontname="arial", fontsize=10)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_1e.pdf')

jpm_data['Log Returns'].plot(color = 'red')

plt.title('Log Returns for J.P. Morgan', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=12)
plt.ylabel('Log Returns', fontname="arial", fontsize=12)
plt.xticks(fontname="arial", fontsize=10)
plt.yticks(fontname="arial", fontsize=10)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_1f.pdf')

dji_data['Simple Returns'].plot(color = 'blue')

plt.title('Simple Returns for the Dow Jones Index', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=12)
plt.ylabel('Simple Returns', fontname="arial", fontsize=12)
plt.xticks(fontname="arial", fontsize=10)
plt.yticks(fontname="arial", fontsize=10)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_1g.pdf')

dji_data['Log Returns'].plot(color = 'red')

plt.title('Log Returns for the Dow Jones Index', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=12)
plt.ylabel('Log Returns', fontname="arial", fontsize=12)
plt.xticks(fontname="arial", fontsize=10)
plt.yticks(fontname="arial", fontsize=10)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_1h.pdf')

4.1.2

import seaborn as sns 
sns.distplot(apple_data['Simple Returns'], hist=True, kde=True, bins=30, vertical = False, color = 'red', hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2})

plt.title('Histogram and PDF of Simple Returns of AAPL based on Adj. Close Prices', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Simple Return', fontname="arial", fontsize=14)
plt.ylabel('Density', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=12)
plt.yticks(fontname="arial", fontsize=12)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(7.1, 4.5)

# plt.savefig('4_1_2a.pdf')

/opt/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

sns.distplot(apple_data['Adj Close'], hist=True, kde=True, bins=40, color = 'blue', hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2})

# plt.hist(apple_data['Adj Close'] , bins = 30)


plt.title('Histogram and PDF of Adj. Close Prices of AAPL', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Adj Close Prices', fontname="arial", fontsize=14)
plt.ylabel('Density', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=12)
plt.yticks(fontname="arial", fontsize=12)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(7.1, 4.5)
# plt.savefig('4_1_2b.pdf')

/opt/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

import seaborn as sns 
sns.distplot(ibm_data['Simple Returns'], hist=True, kde=True, bins=40, color = 'red', hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2})

plt.title('Histogram and PDF of Simple Returns of IBM based on Adj. Close Prices', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Simple Return', fontname="arial", fontsize=14)
plt.ylabel('Density', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=12)
plt.yticks(fontname="arial", fontsize=12)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(7.1, 4.5)

# plt.savefig('4_1_2c.pdf')

/opt/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

sns.distplot(ibm_data['Adj Close'], hist=True, kde=True, bins=40, color = 'blue', hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2})

plt.title('Histogram and PDF of Adj. Close Prices of IBM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Adj Close Prices', fontname="arial", fontsize=14)
plt.ylabel('Density', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=12)
plt.yticks(fontname="arial", fontsize=12)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(7.1, 4.5)
plt.savefig('4_1_2d.pdf')

/opt/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

import seaborn as sns 
sns.distplot(jpm_data['Simple Returns'], hist=True, kde=True, bins=40, color = 'red', hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2})

plt.title('Histogram and PDF of Simple Returns of JPM based on Adj. Close Prices', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Simple Return', fontname="arial", fontsize=14)
plt.ylabel('Density', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=12)
plt.yticks(fontname="arial", fontsize=12)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(7.1, 4.5)

plt.savefig('4_1_2e.pdf')

/opt/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

sns.distplot(jpm_data['Adj Close'], hist=True, kde=True, bins=40, color = 'blue', hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2})

plt.title('Histogram and PDF of Adj. Close Prices of JPM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Adj Close Prices', fontname="arial", fontsize=14)
plt.ylabel('Density', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=12)
plt.yticks(fontname="arial", fontsize=12)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(7.1, 4.5)
plt.savefig('4_1_2f.pdf')

/opt/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

import seaborn as sns 
sns.distplot(dji_data['Simple Returns'], hist=True, kde=True, bins=40, color = 'red', hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2})

plt.title('Histogram and PDF of Simple Returns of DJI based on Adj. Close Prices', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Simple Return', fontname="arial", fontsize=14)
plt.ylabel('Density', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=12)
plt.yticks(fontname="arial", fontsize=12)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(7.1, 4.5)

plt.savefig('4_1_2g.pdf')

/opt/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

sns.distplot(dji_data['Adj Close'], hist=True, kde=True, bins=40, color = 'blue', hist_kws={'edgecolor':'black'}, kde_kws={'linewidth': 2})

plt.title('Histogram and PDF of Adj. Close Prices of DJI', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Adj Close Prices', fontname="arial", fontsize=14)
plt.ylabel('Density', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=12)
plt.yticks(fontname="arial", fontsize=12)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

fig = plt.gcf()
fig.set_size_inches(7.1, 4.5)
plt.savefig('4_1_2h.pdf')

/opt/anaconda3/lib/python3.8/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
  warnings.warn(msg, FutureWarning)

4.1.3

rolling_mean = apple_data['Adj Close'].rolling(5).mean().dropna()
rolling_std = apple_data['Adj Close'].rolling(5).std().dropna()

apple_data['Adj Close'].plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_mean + (1.5*rolling_std)).plot(color = 'green')
(rolling_mean - (1.5*rolling_std)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Mean and ±1.5 Std. Relative to Rolling Mean for AAPL', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Mean', 'Upper Bound (Std)', 'Lower Bound (Std)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

# plt.savefig('4_1_3a.pdf')

rolling_mean = ibm_data['Adj Close'].rolling(5).mean().dropna()
rolling_std = ibm_data['Adj Close'].rolling(5).std().dropna()

ibm_data['Adj Close'].plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_mean + (1.5*rolling_std)).plot(color = 'green')
(rolling_mean - (1.5*rolling_std)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Mean and ±1.5 Std. Relative to Rolling Mean for IBM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Mean', 'Upper Bound (Std)', 'Lower Bound (Std)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_3b.pdf')

rolling_mean = jpm_data['Adj Close'].rolling(5).mean().dropna()
rolling_std = jpm_data['Adj Close'].rolling(5).std().dropna()

jpm_data['Adj Close'].plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_mean + (1.5*rolling_std)).plot(color = 'green')
(rolling_mean - (1.5*rolling_std)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Mean and ±1.5 Std. Relative to Rolling Mean for JPM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Mean', 'Upper Bound (Std)', 'Lower Bound (Std)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_3c.pdf')

rolling_mean = dji_data['Adj Close'].rolling(5).mean().dropna()
rolling_std = dji_data['Adj Close'].rolling(5).std().dropna()

dji_data['Adj Close'].plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_mean + (1.5*rolling_std)).plot(color = 'green')
(rolling_mean - (1.5*rolling_std)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Mean and ±1.5 Std. Relative to Rolling Mean for DJI', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Mean', 'Upper Bound (Std)', 'Lower Bound (Std)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_3d.pdf')

adjClose = apple_data['Adj Close'].copy() 
rolling_mean = adjClose.rolling(5).mean()
rolling_std = adjClose.rolling(5).std()

x = len(adjClose[adjClose > (rolling_mean + (1.5*rolling_std))]) + len(adjClose[adjClose < (rolling_mean - (1.5*rolling_std))])
print(x)

30

adjClose = ibm_data['Adj Close'].copy() 
rolling_mean = adjClose.rolling(5).mean()
rolling_std = adjClose.rolling(5).std()

x = len(adjClose[adjClose > (rolling_mean + (1.5*rolling_std))]) + len(adjClose[adjClose < (rolling_mean - (1.5*rolling_std))])
print(x)

31

adjClose = jpm_data['Adj Close'].copy() 
rolling_mean = adjClose.rolling(5).mean()
rolling_std = adjClose.rolling(5).std()

x = len(adjClose[adjClose > (rolling_mean + (1.5*rolling_std))]) + len(adjClose[adjClose < (rolling_mean - (1.5*rolling_std))])
print(x)

33

adjClose = dji_data['Adj Close'].copy() 
rolling_mean = adjClose.rolling(5).mean()
rolling_std = adjClose.rolling(5).std()

x = len(adjClose[adjClose > (rolling_mean + (1.5*rolling_std))]) + len(adjClose[adjClose < (rolling_mean - (1.5*rolling_std))])
print(x)

30

rolling_median = apple_data['Adj Close'].rolling(5).median().dropna()
rolling_mad = abs(apple_data['Adj Close'] -  apple_data['Adj Close'].rolling(5).median()).median()

apple_data['Adj Close'].plot(color = 'red')
rolling_median.plot(color = 'blue')
(rolling_median + (1.5*rolling_mad)).plot(color = 'green')
(rolling_median - (1.5*rolling_mad)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Median and ±1.5 Rolling MAD for AAPL', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Median', 'Upper Bound (MAD)', 'Lower Bound (MAD)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_3e.pdf')

rolling_median = ibm_data['Adj Close'].rolling(5).median().dropna()
rolling_mad = abs(ibm_data['Adj Close'] -  ibm_data['Adj Close'].rolling(5).median()).median()

ibm_data['Adj Close'].plot(color = 'red')
rolling_median.plot(color = 'blue')
(rolling_median + (1.5*rolling_mad)).plot(color = 'green')
(rolling_median - (1.5*rolling_mad)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Median and ±1.5 Rolling MAD for IBM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Median', 'Upper Bound (MAD)', 'Lower Bound (MAD)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_3f.pdf')

rolling_median = jpm_data['Adj Close'].rolling(5).median().dropna()
rolling_mad = abs(jpm_data['Adj Close'] -  jpm_data['Adj Close'].rolling(5).median()).median()

jpm_data['Adj Close'].plot(color = 'red')
rolling_median.plot(color = 'blue')
(rolling_median + (1.5*rolling_mad)).plot(color = 'green')
(rolling_median - (1.5*rolling_mad)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Median and ±1.5 Rolling MAD for JPM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Median', 'Upper Bound (MAD)', 'Lower Bound (MAD)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_3g.pdf')

rolling_median = dji_data['Adj Close'].rolling(5).median().dropna()
rolling_mad = abs(dji_data['Adj Close'] -  dji_data['Adj Close'].rolling(5).median()).median()

dji_data['Adj Close'].plot(color = 'red')
rolling_median.plot(color = 'blue')
(rolling_median + (1.5*rolling_mad)).plot(color = 'green')
(rolling_median - (1.5*rolling_mad)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Median and ±1.5 Rolling MAD for DJI', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Median', 'Upper Bound (MAD)', 'Lower Bound (MAD)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_3h.pdf')

adjClose = apple_data['Adj Close'].copy() 

rolling_median = adjClose.rolling(5).median() 
rolling_mad = abs(adjClose -  adjClose.rolling(5).median()).median()

x = len(adjClose[adjClose > (rolling_median + (1.5*rolling_mad))]) + len(adjClose[adjClose < (rolling_median - (1.5*rolling_mad))])
print(x)

90

adjClose = ibm_data['Adj Close'].copy() 

rolling_median = adjClose.rolling(5).median() 
rolling_mad = abs(adjClose -  adjClose.rolling(5).median()).median()

x = len(adjClose[adjClose > (rolling_median + (1.5*rolling_mad))]) + len(adjClose[adjClose < (rolling_median - (1.5*rolling_mad))])
print(x)

89

adjClose = jpm_data['Adj Close'].copy() 

rolling_median = adjClose.rolling(5).median() 
rolling_mad = abs(adjClose -  adjClose.rolling(5).median()).median()

x = len(adjClose[adjClose > (rolling_median + (1.5*rolling_mad))]) + len(adjClose[adjClose < (rolling_median - (1.5*rolling_mad))])
print(x)

92

adjClose = dji_data['Adj Close'].copy() 

rolling_median = adjClose.rolling(5).median() 
rolling_mad = abs(adjClose -  adjClose.rolling(5).median()).median()

x = len(adjClose[adjClose > (rolling_median + (1.5*rolling_mad))]) + len(adjClose[adjClose < (rolling_median - (1.5*rolling_mad))])
print(x)

80

4.1.4

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

apple_data_outlier = apple_data.copy() 
apple_data_outlier_close = apple_data_outlier['Adj Close']

max_value = apple_data_outlier_close.max() 

for date in dates:
    apple_data_outlier_close[date] = 1.2 * max_value

rolling_mean = apple_data_outlier_close.rolling(5).mean().dropna()
rolling_std = apple_data_outlier_close.rolling(5).std().dropna()

apple_data_outlier_close.plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_mean + (1.5*rolling_std)).plot(color = 'green')
(rolling_mean - (1.5*rolling_std)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Mean and ±1.5 Rolling Std. Dev for AAPL', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=16)
plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Mean', 'Upper Bound (Std)', 'Lower Bound (Std)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_4a.pdf')

<ipython-input-39-12e071828b9c>:9: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data_outlier_close[date] = 1.2 * max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

apple_data_outlier = apple_data.copy() 
apple_data_outlier_close = apple_data_outlier['Adj Close']

max_value = apple_data_outlier_close.max() 

for date in dates:
    apple_data_outlier_close[date] = 1.2 * max_value

rolling_median = apple_data_outlier_close.rolling(5).median().dropna()
rolling_mad = abs(apple_data_outlier_close -  rolling_median).median()

apple_data_outlier_close.plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_median + (1.5*rolling_mad)).plot(color = 'green')
(rolling_median - (1.5*rolling_mad)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Median and ±1.5 Rolling MAD for AAPL', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=16)
plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Median', 'Upper Bound (MAD)', 'Lower Bound (MAD)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_4b.pdf')
    

<ipython-input-40-4af550c3ab7e>:9: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data_outlier_close[date] = 1.2 * max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

ibm_data_outlier = ibm_data.copy() 
ibm_data_outlier_close = ibm_data_outlier['Adj Close']

max_value = ibm_data_outlier_close.max() 

for date in dates:
    ibm_data_outlier_close[date] = 1.2 * max_value

rolling_mean = ibm_data_outlier_close.rolling(5).mean().dropna()
rolling_std = ibm_data_outlier_close.rolling(5).std().dropna()

ibm_data_outlier_close.plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_mean + (1.5*rolling_std)).plot(color = 'green')
(rolling_mean - (1.5*rolling_std)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Mean and ±1.5 Rolling Std. Dev for IBM', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=16)
plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Mean', 'Upper Bound (Std)', 'Lower Bound (Std)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_4c.pdf')

<ipython-input-41-10985dbd36cf>:9: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  ibm_data_outlier_close[date] = 1.2 * max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

ibm_data_outlier = ibm_data.copy() 
ibm_data_outlier_close = ibm_data_outlier['Adj Close']

max_value = ibm_data_outlier_close.max() 

for date in dates:
    ibm_data_outlier_close[date] = 1.2 * max_value

rolling_median = ibm_data_outlier_close.rolling(5).median().dropna()
rolling_mad = abs(ibm_data_outlier_close -  rolling_median).median()

ibm_data_outlier_close.plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_median + (1.5*rolling_mad)).plot(color = 'green')
(rolling_median - (1.5*rolling_mad)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Median and ±1.5 Rolling MAD for IBM', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=16)
plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Median', 'Upper Bound (MAD)', 'Lower Bound (MAD)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_4d.pdf')
    

<ipython-input-42-b33961ee34b5>:9: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  ibm_data_outlier_close[date] = 1.2 * max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

jpm_data_outlier = jpm_data.copy() 
jpm_data_outlier_close = jpm_data_outlier['Adj Close']

max_value = jpm_data_outlier_close.max() 

for date in dates:
    jpm_data_outlier_close[date] = 1.2 * max_value

rolling_mean = jpm_data_outlier_close.rolling(5).mean().dropna()
rolling_std = jpm_data_outlier_close.rolling(5).std().dropna()

jpm_data_outlier_close.plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_mean + (1.5*rolling_std)).plot(color = 'green')
(rolling_mean - (1.5*rolling_std)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Mean and ±1.5 Rolling Std. Dev for JPM', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=16)
plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Mean', 'Upper Bound (Std)', 'Lower Bound (Std)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_4e.pdf')

<ipython-input-43-c4b5eb4edb74>:9: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  jpm_data_outlier_close[date] = 1.2 * max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

jpm_data_outlier = jpm_data.copy() 
jpm_data_outlier_close = jpm_data_outlier['Adj Close']

max_value = jpm_data_outlier_close.max() 

for date in dates:
    jpm_data_outlier_close[date] = 1.2 * max_value

rolling_median = jpm_data_outlier_close.rolling(5).median().dropna()
rolling_mad = abs(jpm_data_outlier_close -  rolling_median).median()

jpm_data_outlier_close.plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_median + (1.5*rolling_mad)).plot(color = 'green')
(rolling_median - (1.5*rolling_mad)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Median and ±1.5 Rolling MAD for JPM', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=16)
plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Median', 'Upper Bound (MAD)', 'Lower Bound (MAD)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_4f.pdf')
    

<ipython-input-44-13b987dd9821>:9: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  jpm_data_outlier_close[date] = 1.2 * max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

dji_data_outlier = dji_data.copy() 
dji_data_outlier_close = dji_data_outlier['Adj Close']

max_value = dji_data_outlier_close.max() 

for date in dates:
    dji_data_outlier_close[date] = 1.2 * max_value

rolling_mean = dji_data_outlier_close.rolling(5).mean().dropna()
rolling_std = dji_data_outlier_close.rolling(5).std().dropna()

dji_data_outlier_close.plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_mean + (1.5*rolling_std)).plot(color = 'green')
(rolling_mean - (1.5*rolling_std)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Mean and ±1.5 Rolling Std. Dev for DJI', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=16)
plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Mean', 'Upper Bound (Std)', 'Lower Bound (Std)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_4g.pdf')

<ipython-input-45-4fba357efef7>:9: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  dji_data_outlier_close[date] = 1.2 * max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

dji_data_outlier = dji_data.copy() 
dji_data_outlier_close = dji_data_outlier['Adj Close']

max_value = dji_data_outlier_close.max() 

for date in dates:
    dji_data_outlier_close[date] = 1.2 * max_value

rolling_median = dji_data_outlier_close.rolling(5).median().dropna()
rolling_mad = abs(dji_data_outlier_close -  rolling_median).median()

dji_data_outlier_close.plot(color = 'red')
rolling_mean.plot(color = 'blue')
(rolling_median + (1.5*rolling_mad)).plot(color = 'green')
(rolling_median - (1.5*rolling_mad)).plot(color = 'orange')

plt.title('Adj. Close Prices, 5-Day Rolling Median and ±1.5 Rolling MAD for DJI', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=16)
plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)

plt.legend(['Adj Close Price', 'Rolling Median', 'Upper Bound (MAD)', 'Lower Bound (MAD)'])

fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_1_4h.pdf')
    

<ipython-input-46-750adb28d049>:9: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  dji_data_outlier_close[date] = 1.2 * max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

4.1.5

import matplotlib.pyplot as plt
adjClose = apple_data['Adj Close'].copy() 
plt.boxplot(adjClose)

plt.title('Box Plot for Apple', fontname="arial", fontsize=16, fontweight="bold")

plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_5a.pdf')

adjClose = ibm_data['Adj Close'].copy() 
plt.boxplot(adjClose)

plt.title('Box Plot for IBM', fontname="arial", fontsize=16, fontweight="bold")

plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_5b.pdf')

adjClose = jpm_data['Adj Close'].copy() 
plt.boxplot(adjClose)

plt.title('Box Plot for J.P. Morgan', fontname="arial", fontsize=16, fontweight="bold")

plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_5c.pdf')

adjClose = dji_data['Adj Close'].copy() 
plt.boxplot(adjClose)

plt.title('Box Plot for the Dow Jones Index', fontname="arial", fontsize=16, fontweight="bold")

plt.ylabel('Price', fontname="arial", fontsize=16)
plt.xticks(fontname="arial", fontsize=16)
plt.yticks(fontname="arial", fontsize=16)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
fig = plt.gcf()
fig.set_size_inches(6, 4)

plt.savefig('4_1_5d.pdf')

4.2 Robust Estimators

4.2.1

def med(df): 
    df_sorted = df.sort_values()
    middle_index = round(len(df_sorted) / 2)
    return df_sorted[middle_index]

def interquartile_range(df):
    df_sorted = df.sort_values()
    quarter_index = round(len(df_sorted) / 4) 
    three_quarter_index = round(3 * len(df_sorted) / 4)
    Q25 = df_sorted[quarter_index]
    Q75 = df_sorted[three_quarter_index]
    return Q75 - Q25

def median_absolute_deviation(df):
    initial_median = med(df)
    absolute_deviations = abs(df - initial_median)
    return med(absolute_deviations)
    

4.3 Robust and OLS Regression

4.3.1

from sklearn import linear_model

ret_stock = apple_data[['Simple Returns']].dropna()
ret_dji = dji_data[['Simple Returns']].dropna()

regress = linear_model.LinearRegression() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

plt.plot(ret_stock.index, y, color = 'blue')
plt.plot(ret_stock.index, predict, color = 'orange')
plt.legend(['Simple Returns','Predicted Returns'])

plt.title('Predicted Returns of Apple using OLS', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

print("Intercept:", intercept)
print("Coefficient:", coefficient)

# plt.savefig('4_3_1a.pdf')
print("R-Squared Score: ", regress.score(X, y))

Intercept: 0.00016466014892917348
Coefficient: 1.3255798434655275
R-Squared Score:  0.5165176143267884

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['OLS Prediction', 'Actual Scatter'])

plt.title('OLS Regression of Apple Simple Returns vs DJI Simple Returns', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('Apple Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)



fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_3_1b.pdf')
    

from sklearn import linear_model

ret_stock = ibm_data[['Simple Returns']].dropna()
ret_dji = dji_data[['Simple Returns']].dropna()

regress = linear_model.LinearRegression() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

plt.plot(ret_stock.index, y, color = 'blue')
plt.plot(ret_stock.index, predict, color = 'orange')
plt.legend(['Simple Returns','Predicted Returns'])

plt.title('Predicted Returns of IBM using OLS', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

print("Intercept:", intercept)
print("Coefficient:", coefficient)

# plt.savefig('4_3_1c.pdf')
print("R-Squared Score: ", regress.score(X, y))

Intercept: -0.000440572495482164
Coefficient: 0.9600924554800796
R-Squared Score:  0.4177725981268693

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['OLS Prediction', 'Actual Scatter'])

plt.title('OLS Regression of IBM Simple Returns vs DJI Simple Returns', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('IBM Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)



fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_3_1d.pdf')
    

from sklearn import linear_model

ret_stock = jpm_data[['Simple Returns']].dropna()
ret_dji = dji_data[['Simple Returns']].dropna()

regress = linear_model.LinearRegression() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

plt.plot(ret_stock.index, y, color = 'blue')
plt.plot(ret_stock.index, predict, color = 'orange')
plt.legend(['Simple Returns','Predicted Returns'])

plt.title('Predicted Returns of J.P. Morgan using OLS', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

print("Intercept:", intercept)
print("Coefficient:", coefficient)

# plt.savefig('4_3_1e.pdf')
print("R-Squared Score: ", regress.score(X, y))

Intercept: -0.00031633075996005287
Coefficient: 0.9314081808843367
R-Squared Score:  0.5558638461848688

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['OLS Prediction', 'Actual Scatter'])

plt.title('OLS Regression of J.P. Morgan Simple Returns vs DJI Simple Returns', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('J.P. Morgan Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)



fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_3_1f.pdf')
    

4.3.2

from sklearn import linear_model

ret_stock = apple_data[['Simple Returns']].dropna()
ret_dji = dji_data[['Simple Returns']].dropna()

regress = linear_model.HuberRegressor() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

plt.plot(ret_stock.index, y, color = 'blue')
plt.plot(ret_stock.index, predict, color = 'orange')
plt.legend(['Simple Returns','Predicted Returns'])

plt.title('Predicted Returns of Apple using Huber Regression', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

print("Intercept:", intercept)
print("Coefficient:", coefficient)

# plt.savefig('4_3_2a.pdf')
print("R-Squared Score: ", regress.score(X, y))

/opt/anaconda3/lib/python3.8/site-packages/sklearn/utils/validation.py:72: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  return f(**kwargs)

Intercept: -0.00013037065614373493
Coefficient: 1.2702124335516514
R-Squared Score:  0.5153648281193706

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['Huber Regression Prediction', 'Actual Scatter'])

plt.title('Huber Regression of Apple Simple Returns vs DJI Simple Returns', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('Apple Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_3_2b.pdf')
    

from sklearn import linear_model

ret_stock = ibm_data[['Simple Returns']].dropna()
ret_dji = dji_data[['Simple Returns']].dropna()

regress = linear_model.HuberRegressor() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

plt.plot(ret_stock.index, y, color = 'blue')
plt.plot(ret_stock.index, predict, color = 'orange')
plt.legend(['Simple Returns','Predicted Returns'])

plt.title('Predicted Returns of IBM using Huber Regression', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

print("Intercept:", intercept)
print("Coefficient:", coefficient)

# plt.savefig('4_3_2c.pdf')
print("R-Squared Score: ", regress.score(X, y))

/opt/anaconda3/lib/python3.8/site-packages/sklearn/utils/validation.py:72: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  return f(**kwargs)

Intercept: -0.0005094349614468659
Coefficient: 0.9735620712623559
R-Squared Score:  0.4176721932886538

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['Huber Regression Prediction', 'Actual Scatter'])

plt.title('Huber Regression of IBM Simple Returns vs DJI Simple Returns', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('IBM Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_3_2d.pdf')
    

from sklearn import linear_model

ret_stock = jpm_data[['Simple Returns']].dropna()
ret_dji = dji_data[['Simple Returns']].dropna()

regress = linear_model.HuberRegressor() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

plt.plot(ret_stock.index, y, color = 'blue')
plt.plot(ret_stock.index, predict, color = 'orange')
plt.legend(['Simple Returns','Predicted Returns'])

plt.title('Predicted Returns of J.P. Morgan using Huber Regression', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

print("Intercept:", intercept)
print("Coefficient:", coefficient)

# plt.savefig('4_3_2e.pdf')
print("R-Squared Score: ", regress.score(X, y))

/opt/anaconda3/lib/python3.8/site-packages/sklearn/utils/validation.py:72: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  return f(**kwargs)

Intercept: -0.0008009614209572162
Coefficient: 0.9196620617499993
R-Squared Score:  0.5543856144824422

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['Huber Regression Prediction', 'Actual Scatter'])

plt.title('Huber Regression of J.P. Morgan Simple Returns vs DJI Simple Returns', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('J.P. Morgan Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_3_2f.pdf')
    

4.3.3

from sklearn import linear_model
import numpy as np 
import pandas as pd 
from statsmodels import robust
from scipy.stats import iqr
from scipy import stats
import matplotlib.pyplot as plt

AAPL = pd.read_csv('AAPL.csv', index_col=0) 
IBM = pd.read_csv('IBM.csv', index_col=0) 
JPM = pd.read_csv('JPM.csv', index_col=0) 
DJI = pd.read_csv('DJI.csv', index_col=0)

AAPL.index = pd.to_datetime(AAPL.index)
IBM.index = pd.to_datetime(IBM.index)
DJI.index = pd.to_datetime(DJI.index)
JPM.index = pd.to_datetime(JPM.index)

apple_data = AAPL.copy() 
ibm_data = IBM.copy() 
dji_data = DJI.copy() 
jpm_data = JPM.copy() 


dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


stock_data_outlier = apple_data.copy() 
dji_data_outlier = dji_data.copy() 

stock_data_outlier['Simple Returns'] = stock_data_outlier['Adj Close'].pct_change() 
dji_data_outlier['Simple Returns'] = dji_data_outlier['Adj Close'].pct_change() 

stock_max_value = stock_data_outlier['Adj Close'].max()
dji_max_value = dji_data_outlier['Adj Close'].max()

for date in dates:
    stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value

stock_data_outlier['Simple Returns Modified'] = stock_data_outlier['Adj Close'].dropna().pct_change()     
dji_data_outlier['Simple Returns Modified'] = dji_data_outlier['Adj Close'].dropna().pct_change()     


ret_stock = stock_data_outlier[['Simple Returns Modified']].dropna()
ret_dji = dji_data_outlier[['Simple Returns Modified']].dropna()

regress = linear_model.LinearRegression() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

print("Intercept: ", intercept)
print("Coefficient:", coefficient)
print("R-Squared Score: ", regress.score(X, y))

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['OLS Prediction', 'Actual Scatter'])

plt.title('OLS Regression of Apple Simple Returns vs DJI Simple Returns with Outliers', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('Apple Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)
plt.ylim([-0.1, 0.08])


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_3_3a.pdf')

<ipython-input-64-5eef0dc9c733>:38: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

Intercept:  0.003549490722840998
Coefficient: 1.0898121696643095
R-Squared Score:  0.016532159461199125

from sklearn import linear_model

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']
stock_data_outlier = ibm_data.copy() 
dji_data_outlier = dji_data.copy() 

stock_data_outlier['Simple Returns'] = stock_data_outlier['Adj Close'].pct_change() 
dji_data_outlier['Simple Returns'] = dji_data_outlier['Adj Close'].pct_change() 

stock_max_value = stock_data_outlier['Adj Close'].max()
dji_max_value = dji_data_outlier['Adj Close'].max()

for date in dates:
    stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value

stock_data_outlier['Simple Returns Modified'] = stock_data_outlier['Adj Close'].dropna().pct_change()     
dji_data_outlier['Simple Returns Modified'] = dji_data_outlier['Adj Close'].dropna().pct_change()     


ret_stock = stock_data_outlier[['Simple Returns Modified']].dropna()
ret_dji = dji_data_outlier[['Simple Returns Modified']].dropna()

regress = linear_model.LinearRegression() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

print("Intercept: ", intercept)
print("Coefficient:", coefficient)
print("R-Squared Score: ", regress.score(X, y))

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['OLS Prediction', 'Actual Scatter'])

plt.title('OLS Regression of IBM Simple Returns vs DJI Simple Returns with Outliers', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('IBM Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)
plt.ylim([-0.08, 0.08])


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_3_3b.pdf')

<ipython-input-65-fcc475885032>:14: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

Intercept:  0.0017162600387344896
Coefficient: 0.7904432787562923
R-Squared Score:  0.014326326309465842

from sklearn import linear_model

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']
stock_data_outlier = jpm_data.copy() 
dji_data_outlier = dji_data.copy() 

stock_data_outlier['Simple Returns'] = stock_data_outlier['Adj Close'].pct_change() 
dji_data_outlier['Simple Returns'] = dji_data_outlier['Adj Close'].pct_change() 

stock_max_value = stock_data_outlier['Adj Close'].max()
dji_max_value = dji_data_outlier['Adj Close'].max()

for date in dates:
    stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value

stock_data_outlier['Simple Returns Modified'] = stock_data_outlier['Adj Close'].dropna().pct_change()     
dji_data_outlier['Simple Returns Modified'] = dji_data_outlier['Adj Close'].dropna().pct_change()     


ret_stock = stock_data_outlier[['Simple Returns Modified']].dropna()
ret_dji = dji_data_outlier[['Simple Returns Modified']].dropna()

regress = linear_model.LinearRegression() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

print("Intercept: ", intercept)
print("Coefficient:", coefficient)
print("R-Squared Score: ", regress.score(X, y))

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['OLS Prediction', 'Actual Scatter'])

plt.title('OLS Regression of JPM Simple Returns vs DJI Simple Returns with Outliers', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('J.P. Morgan Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)
plt.ylim([-0.04, 0.04])


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_3_3c.pdf')

<ipython-input-66-e60ec39fbbbc>:14: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

Intercept:  0.0010421467748870134
Coefficient: 0.8435894617700498
R-Squared Score:  0.026162346446048867

from sklearn import linear_model

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']
stock_data_outlier = apple_data.copy() 
dji_data_outlier = dji_data.copy() 

stock_data_outlier['Simple Returns'] = stock_data_outlier['Adj Close'].pct_change() 
dji_data_outlier['Simple Returns'] = dji_data_outlier['Adj Close'].pct_change() 

stock_max_value = stock_data_outlier['Adj Close'].max()
dji_max_value = dji_data_outlier['Adj Close'].max()

for date in dates:
    stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value

stock_data_outlier['Simple Returns Modified'] = stock_data_outlier['Adj Close'].dropna().pct_change()     
dji_data_outlier['Simple Returns Modified'] = dji_data_outlier['Adj Close'].dropna().pct_change()     


ret_stock = stock_data_outlier[['Simple Returns Modified']].dropna()
ret_dji = dji_data_outlier[['Simple Returns Modified']].dropna()

regress = linear_model.HuberRegressor() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

print("Intercept: ", intercept)
print("Coefficient:", coefficient)
print("R-Squared Score: ", regress.score(X, y))

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['Huber Prediction', 'Actual Scatter'])

plt.title('Huber Regression of Apple Simple Returns vs DJI Simple Returns with Outliers', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('Apple Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)
plt.ylim([-0.1, 0.075])


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_3_3d.pdf')

<ipython-input-67-aae10690ba0a>:14: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)
/opt/anaconda3/lib/python3.8/site-packages/sklearn/utils/validation.py:72: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  return f(**kwargs)

Intercept:  7.5229485921091805e-06
Coefficient: 1.269470572076923
R-Squared Score:  0.014517140673291018

from sklearn import linear_model

dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']
stock_data_outlier = ibm_data.copy() 
dji_data_outlier = dji_data.copy() 

stock_data_outlier['Simple Returns'] = stock_data_outlier['Adj Close'].pct_change() 
dji_data_outlier['Simple Returns'] = dji_data_outlier['Adj Close'].pct_change() 

stock_max_value = stock_data_outlier['Adj Close'].max()
dji_max_value = dji_data_outlier['Adj Close'].max()

for date in dates:
    stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value

stock_data_outlier['Simple Returns Modified'] = stock_data_outlier['Adj Close'].dropna().pct_change()     
dji_data_outlier['Simple Returns Modified'] = dji_data_outlier['Adj Close'].dropna().pct_change()     


ret_stock = stock_data_outlier[['Simple Returns Modified']].dropna()
ret_dji = dji_data_outlier[['Simple Returns Modified']].dropna()

regress = linear_model.HuberRegressor() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)
print("Intercept: ", intercept)
print("Coefficient:", coefficient)
print("R-Squared Score: ", regress.score(X, y))

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['Huber Prediction', 'Actual Scatter'])

plt.title('Huber Regression of IBM Simple Returns vs DJI Simple Returns with Outliers', fontname="arial", fontsize=14, fontweight="bold")
plt.ylim([-0.08, 0.08])

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('IBM Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)

plt.savefig('4_3_3e.pdf')

<ipython-input-68-72f301905917>:14: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)
/opt/anaconda3/lib/python3.8/site-packages/sklearn/utils/validation.py:72: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  return f(**kwargs)

Intercept:  -0.0005072169944084335
Coefficient: 0.9738519062813633
R-Squared Score:  0.01255141281946115

from sklearn import linear_model

dates = ['2018-05-14', '2018-06-17', '2018-09-14', '2018-12-14', '2019-01-14', '2019-02-14', '2018-06-13', '2018-06-20']
stock_data_outlier = jpm_data.copy() 
dji_data_outlier = dji_data.copy() 

stock_data_outlier['Simple Returns'] = stock_data_outlier['Adj Close'].pct_change() 
dji_data_outlier['Simple Returns'] = dji_data_outlier['Adj Close'].pct_change() 

stock_max_value = stock_data_outlier['Adj Close'].max()
dji_max_value = dji_data_outlier['Adj Close'].max()

for date in dates:
    stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value

stock_data_outlier['Simple Returns Modified'] = stock_data_outlier['Adj Close'].dropna().pct_change()     
dji_data_outlier['Simple Returns Modified'] = dji_data_outlier['Adj Close'].dropna().pct_change()     


ret_stock = stock_data_outlier[['Simple Returns Modified']].dropna()
ret_dji = dji_data_outlier[['Simple Returns Modified']].dropna()

regress = linear_model.HuberRegressor() 

X = ret_dji.copy().values.reshape(-1, 1)
y = ret_stock.copy().values.reshape(-1, 1)

regress.fit(X, y) 

predict = regress.predict(X) 

intercept = float(regress.intercept_)
coefficient = float(regress.coef_)

print("Intercept: ", intercept)
print("Coefficient:", coefficient)
print("R-Squared Score: ", regress.score(X, y))

plt.scatter(X, y, color = 'blue')
plt.plot(X, predict, color = 'red')
plt.legend(['Huber Prediction', 'Actual Scatter'])
plt.ylim([-0.04, 0.04])
plt.xlim([-0.03, 0.05])

plt.title('Huber Regression of JPM Simple Returns vs DJI Simple Returns with Outliers', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('DJI Daily Simple Returns', fontname="arial", fontsize=14)
plt.ylabel('J.P. Morgan Daily Simple Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_3_3f.pdf')

<ipython-input-69-a70e96b68951>:14: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  stock_data_outlier['Adj Close'][date] = 1.2 * stock_max_value
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)
/opt/anaconda3/lib/python3.8/site-packages/sklearn/utils/validation.py:72: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().
  return f(**kwargs)

Intercept:  -0.0010399307087863468
Coefficient: 0.9320167989688328
R-Squared Score:  0.004331192488909341

4.4 Robust Trading Strategies

4.4.1

apple_data = pd.read_csv('AAPL.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)

adjClose = apple_data['Adj Close'].dropna()
apple_data['Ret'] = apple_data['Adj Close'].pct_change() 

MA20 = adjClose.rolling(20).mean()
MA50 = adjClose.rolling(50).mean()

adjClose.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'MA20', 'MA50', 'Buy', 'Sell'])

plt.title('Moving Average Crossover Strategy for Apple', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1a.pdf')

apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).mean().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).mean().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Returns of Apple using Moving Average Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1b.pdf')

apple_data = pd.read_csv('AAPL.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)
adjClose = apple_data['Adj Close'].dropna()

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


adjClose_outlier = adjClose.copy()
max_value = adjClose_outlier.max()

for date in dates:
    adjClose_outlier[date] = max_value * 1.2

MA20 = adjClose_outlier.rolling(20).mean()
MA50 = adjClose_outlier.rolling(50).mean()

adjClose_outlier.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'MA20', 'MA50', 'Buy', 'Sell'])

plt.title('Moving Average Crossover Strategy for Apple with Outliers', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1c.pdf')

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

max_value = apple_data['Adj Close'].max()

for date in dates:
    apple_data['Adj Close'][date] = max_value * 1.2


apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).mean().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).mean().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Return of Apple with Outliers using Moving Average Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1d.pdf')

<ipython-input-73-170362f3c8d8>:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data['Adj Close'][date] = max_value * 1.2
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

apple_data = pd.read_csv('IBM.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)

adjClose = apple_data['Adj Close'].dropna()
apple_data['Ret'] = apple_data['Adj Close'].pct_change() 

MA20 = adjClose.rolling(20).mean()
MA50 = adjClose.rolling(50).mean()

adjClose.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'MA20', 'MA50', 'Buy', 'Sell'])

plt.title('Moving Average Crossover Strategy for IBM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1e.pdf')

apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).mean().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).mean().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Returns of IBM using Moving Average Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1f.pdf')

apple_data = pd.read_csv('IBM.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)
adjClose = apple_data['Adj Close'].dropna()

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


adjClose_outlier = adjClose.copy()
max_value = adjClose_outlier.max()

for date in dates:
    adjClose_outlier[date] = max_value * 1.2

MA20 = adjClose_outlier.rolling(20).mean()
MA50 = adjClose_outlier.rolling(50).mean()

adjClose_outlier.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'MA20', 'MA50', 'Buy', 'Sell'])

plt.title('Moving Average Crossover Strategy for IBM with Outliers', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1g.pdf')

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

max_value = apple_data['Adj Close'].max()

for date in dates:
    apple_data['Adj Close'][date] = max_value * 1.2


apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).mean().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).mean().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Return of IBM with Outliers using Moving Average Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1h.pdf')

<ipython-input-77-44246cbe3ef3>:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data['Adj Close'][date] = max_value * 1.2
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

apple_data = pd.read_csv('DJI.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)

adjClose = apple_data['Adj Close'].dropna()
apple_data['Ret'] = apple_data['Adj Close'].pct_change() 

MA20 = adjClose.rolling(20).mean()
MA50 = adjClose.rolling(50).mean()

adjClose.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'MA20', 'MA50', 'Buy', 'Sell'])

plt.title('Moving Average Crossover Strategy for DJI', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1i.pdf')

apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).mean().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).mean().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Returns of DJI using Moving Average Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1j.pdf')

apple_data = pd.read_csv('DJI.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)
adjClose = apple_data['Adj Close'].dropna()

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


adjClose_outlier = adjClose.copy()
max_value = adjClose_outlier.max()

for date in dates:
    adjClose_outlier[date] = max_value * 1.2

MA20 = adjClose_outlier.rolling(20).mean()
MA50 = adjClose_outlier.rolling(50).mean()

adjClose_outlier.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'MA20', 'MA50', 'Buy', 'Sell'])

plt.title('Moving Average Crossover Strategy for DJI with Outliers', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1k.pdf')

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

max_value = apple_data['Adj Close'].max()

for date in dates:
    apple_data['Adj Close'][date] = max_value * 1.2


apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).mean().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).mean().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Return of DJI with Outliers using Moving Average Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1l.pdf')

<ipython-input-81-98effbfc3d96>:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data['Adj Close'][date] = max_value * 1.2
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

apple_data = pd.read_csv('JPM.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)

adjClose = apple_data['Adj Close'].dropna()
apple_data['Ret'] = apple_data['Adj Close'].pct_change() 

MA20 = adjClose.rolling(20).mean()
MA50 = adjClose.rolling(50).mean()

adjClose.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'MA20', 'MA50', 'Buy', 'Sell'])

plt.title('Moving Average Crossover Strategy for JPM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1m.pdf')

apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).mean().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).mean().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Returns of JPM using Moving Average Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1n.pdf')

apple_data = pd.read_csv('JPM.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)
adjClose = apple_data['Adj Close'].dropna()

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


adjClose_outlier = adjClose.copy()
max_value = adjClose_outlier.max()

for date in dates:
    adjClose_outlier[date] = max_value * 1.2

MA20 = adjClose_outlier.rolling(20).mean()
MA50 = adjClose_outlier.rolling(50).mean()

adjClose_outlier.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'MA20', 'MA50', 'Buy', 'Sell'])

plt.title('Moving Average Crossover Strategy for JPM with Outliers', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1o.pdf')

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

max_value = apple_data['Adj Close'].max()

for date in dates:
    apple_data['Adj Close'][date] = max_value * 1.2


apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).mean().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).mean().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Return of JPM with Outliers using Moving Average Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_1p.pdf')

<ipython-input-85-b5ffebefc0bf>:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data['Adj Close'][date] = max_value * 1.2
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

4.4.2

apple_data = pd.read_csv('AAPL.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)

adjClose = apple_data['Adj Close'].dropna()
apple_data['Ret'] = apple_data['Adj Close'].pct_change() 

MA20 = adjClose.rolling(20).median()
MA50 = adjClose.rolling(50).median()

adjClose.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'ME20', 'ME50', 'Buy', 'Sell'])

plt.title('Moving Median Crossover Strategy for Apple', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2a.pdf')

apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).median().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).median().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Returns of Apple using Moving Median Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2b.pdf')

apple_data = pd.read_csv('AAPL.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)
adjClose = apple_data['Adj Close'].dropna()

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


adjClose_outlier = adjClose.copy()
max_value = adjClose_outlier.max()

for date in dates:
    adjClose_outlier[date] = max_value * 1.2

MA20 = adjClose_outlier.rolling(20).median()
MA50 = adjClose_outlier.rolling(50).median()

adjClose_outlier.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'ME20', 'ME50', 'Buy', 'Sell'])

plt.title('Moving Median Crossover Strategy for Apple with Outliers', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2c.pdf')

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

max_value = apple_data['Adj Close'].max()

for date in dates:
    apple_data['Adj Close'][date] = max_value * 1.2


apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).median().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).median().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Return of Apple with Outliers using Moving Median Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2d.pdf')

<ipython-input-89-c4f9ede07771>:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data['Adj Close'][date] = max_value * 1.2
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

apple_data = pd.read_csv('IBM.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)

adjClose = apple_data['Adj Close'].dropna()
apple_data['Ret'] = apple_data['Adj Close'].pct_change() 

MA20 = adjClose.rolling(20).median()
MA50 = adjClose.rolling(50).median()

adjClose.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'ME20', 'ME50', 'Buy', 'Sell'])

plt.title('Moving Median Crossover Strategy for IBM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2e.pdf')

apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).median().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).median().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Returns of IBM using Moving Median Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2f.pdf')

apple_data = pd.read_csv('IBM.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)
adjClose = apple_data['Adj Close'].dropna()

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


adjClose_outlier = adjClose.copy()
max_value = adjClose_outlier.max()

for date in dates:
    adjClose_outlier[date] = max_value * 1.2

MA20 = adjClose_outlier.rolling(20).median()
MA50 = adjClose_outlier.rolling(50).median()

adjClose_outlier.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'ME20', 'ME50', 'Buy', 'Sell'])

plt.title('Moving Median Crossover Strategy for IBM with Outliers', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2g.pdf')

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

max_value = apple_data['Adj Close'].max()

for date in dates:
    apple_data['Adj Close'][date] = max_value * 1.2


apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).median().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).median().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Return of IBM with Outliers using Moving Median Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2h.pdf')

<ipython-input-93-c4ac5e891a5c>:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data['Adj Close'][date] = max_value * 1.2
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

apple_data = pd.read_csv('JPM.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)

adjClose = apple_data['Adj Close'].dropna()
apple_data['Ret'] = apple_data['Adj Close'].pct_change() 

MA20 = adjClose.rolling(20).median()
MA50 = adjClose.rolling(50).median()

adjClose.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'ME20', 'ME50', 'Buy', 'Sell'])

plt.title('Moving Median Crossover Strategy for JPM', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2i.pdf')

apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).median().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).median().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Returns of JPM using Moving Median Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2j.pdf')

apple_data = pd.read_csv('JPM.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)
adjClose = apple_data['Adj Close'].dropna()

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


adjClose_outlier = adjClose.copy()
max_value = adjClose_outlier.max()

for date in dates:
    adjClose_outlier[date] = max_value * 1.2

MA20 = adjClose_outlier.rolling(20).median()
MA50 = adjClose_outlier.rolling(50).median()

adjClose_outlier.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'ME20', 'ME50', 'Buy', 'Sell'])

plt.title('Moving Median Crossover Strategy for JPM with Outliers', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2k.pdf')

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

max_value = apple_data['Adj Close'].max()

for date in dates:
    apple_data['Adj Close'][date] = max_value * 1.2


apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).median().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).median().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Return of JPM with Outliers using Moving Median Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2l.pdf')

<ipython-input-97-87992cc63321>:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data['Adj Close'][date] = max_value * 1.2
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)

apple_data = pd.read_csv('DJI.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)

adjClose = apple_data['Adj Close'].dropna()
apple_data['Ret'] = apple_data['Adj Close'].pct_change() 

MA20 = adjClose.rolling(20).median()
MA50 = adjClose.rolling(50).median()

adjClose.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'ME20', 'ME50', 'Buy', 'Sell'])

plt.title('Moving Median Crossover Strategy for DJI', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2m.pdf')

apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).median().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).median().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Returns of DJI using Moving Median Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2n.pdf')

apple_data = pd.read_csv('DJI.csv', index_col=0) 
apple_data.index = pd.to_datetime(apple_data.index)
adjClose = apple_data['Adj Close'].dropna()

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']


adjClose_outlier = adjClose.copy()
max_value = adjClose_outlier.max()

for date in dates:
    adjClose_outlier[date] = max_value * 1.2

MA20 = adjClose_outlier.rolling(20).median()
MA50 = adjClose_outlier.rolling(50).median()

adjClose_outlier.plot(color = 'blue')
MA20.plot(color = 'green')
MA50.plot(color = 'red')

plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 > MA50, color = 'g', alpha = 0.3)
plt.fill_between(adjClose_outlier.index, MA20, MA50, where = MA20 < MA50, color = 'r', alpha = 0.3)


plt.legend(['Adjusted Close Prices', 'ME20', 'ME50', 'Buy', 'Sell'])

plt.title('Moving Median Crossover Strategy for DJI with Outliers', fontname="arial", fontsize=16, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Price', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2o.pdf')

# dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14', '2018-06-21', '2018-10-10', '2018-07-23']
dates = ['2018-05-14', '2018-09-14', '2018-12-14', '2019-01-14']

max_value = apple_data['Adj Close'].max()

for date in dates:
    apple_data['Adj Close'][date] = max_value * 1.2


apple_data['Ret'] = apple_data['Adj Close'].pct_change()
apple_data['Action'] = np.ones(len(apple_data)) * np.nan
apple_data['20 MA'] = apple_data['Adj Close'].rolling(20).median().dropna()
apple_data['50 MA'] = apple_data['Adj Close'].rolling(50).median().dropna()
apple_data.loc[apple_data['20 MA'] >= apple_data['50 MA'], 'Action'] = 1
apple_data.loc[apple_data['20 MA'] < apple_data['50 MA'], 'Action'] = -1
apple_data['cumulative'] = np.cumsum(apple_data['Ret'] * apple_data['Action'])

apple_data['cumulative'].plot(color = 'blue')

plt.title('Cumulative Return of DJI with Outliers using Moving Median Crossover Strategy', fontname="arial", fontsize=14, fontweight="bold")

plt.xlabel('Date', fontname="arial", fontsize=14)
plt.ylabel('Cumulative Returns', fontname="arial", fontsize=14)
plt.xticks(fontname="arial", fontsize=14)
plt.yticks(fontname="arial", fontsize=14)

plt.grid(which='major', linestyle='-', linewidth='0.5', color='#666666')
plt.minorticks_on()
plt.grid(b=True, which='minor', color='#999999', linestyle='-', alpha=0.2)


fig = plt.gcf()
fig.set_size_inches(8, 6)
plt.savefig('4_4_2p.pdf')

<ipython-input-101-0723e5fff1d0>:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  apple_data['Adj Close'][date] = max_value * 1.2
/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexing.py:670: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  iloc._setitem_with_indexer(indexer, value)